theorem Th10:
  for f, g being Real_Sequence
  for n being Nat holds
  (f /" g) . n = (f .n) / (g.n) & (f /" g) . n = (f.n) * (g.n)"
proof
  let f, g;
  let n;
A1: (f /" g). n = (f.n) * (g".n) by SEQ_1:8
    .= (f.n) * (g.n)" by VALUED_1:10;
  hence (f /" g). n = (f.n) / (g.n);
  thus thesis by A1;
end;
